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<li><a class="reference internal" href="#"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.manifold</span></code>.Isomap</a><ul>
<li><a class="reference internal" href="#examples-using-sklearn-manifold-isomap">Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.manifold.Isomap</span></code></a></li>
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  <div class="section" id="sklearn-manifold-isomap">
<h1><a class="reference internal" href="../classes.html#module-sklearn.manifold" title="sklearn.manifold"><code class="xref py py-mod docutils literal notranslate"><span class="pre">sklearn.manifold</span></code></a>.Isomap<a class="headerlink" href="#sklearn-manifold-isomap" title="Permalink to this headline">¶</a></h1>
<dl class="class">
<dt id="sklearn.manifold.Isomap">
<em class="property">class </em><code class="sig-prename descclassname">sklearn.manifold.</code><code class="sig-name descname">Isomap</code><span class="sig-paren">(</span><em class="sig-param">n_neighbors=5</em>, <em class="sig-param">n_components=2</em>, <em class="sig-param">eigen_solver='auto'</em>, <em class="sig-param">tol=0</em>, <em class="sig-param">max_iter=None</em>, <em class="sig-param">path_method='auto'</em>, <em class="sig-param">neighbors_algorithm='auto'</em>, <em class="sig-param">n_jobs=None</em>, <em class="sig-param">metric='minkowski'</em>, <em class="sig-param">p=2</em>, <em class="sig-param">metric_params=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/manifold/_isomap.py#L16"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.manifold.Isomap" title="Permalink to this definition">¶</a></dt>
<dd><p>Isomap Embedding</p>
<p>Non-linear dimensionality reduction through Isometric Mapping</p>
<p>Read more in the <a class="reference internal" href="../manifold.html#isomap"><span class="std std-ref">User Guide</span></a>.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl>
<dt><strong>n_neighbors</strong><span class="classifier">integer</span></dt><dd><p>number of neighbors to consider for each point.</p>
</dd>
<dt><strong>n_components</strong><span class="classifier">integer</span></dt><dd><p>number of coordinates for the manifold</p>
</dd>
<dt><strong>eigen_solver</strong><span class="classifier">[‘auto’|’arpack’|’dense’]</span></dt><dd><p>‘auto’ : Attempt to choose the most efficient solver
for the given problem.</p>
<p>‘arpack’ : Use Arnoldi decomposition to find the eigenvalues
and eigenvectors.</p>
<p>‘dense’ : Use a direct solver (i.e. LAPACK)
for the eigenvalue decomposition.</p>
</dd>
<dt><strong>tol</strong><span class="classifier">float</span></dt><dd><p>Convergence tolerance passed to arpack or lobpcg.
not used if eigen_solver == ‘dense’.</p>
</dd>
<dt><strong>max_iter</strong><span class="classifier">integer</span></dt><dd><p>Maximum number of iterations for the arpack solver.
not used if eigen_solver == ‘dense’.</p>
</dd>
<dt><strong>path_method</strong><span class="classifier">string [‘auto’|’FW’|’D’]</span></dt><dd><p>Method to use in finding shortest path.</p>
<p>‘auto’ : attempt to choose the best algorithm automatically.</p>
<p>‘FW’ : Floyd-Warshall algorithm.</p>
<p>‘D’ : Dijkstra’s algorithm.</p>
</dd>
<dt><strong>neighbors_algorithm</strong><span class="classifier">string [‘auto’|’brute’|’kd_tree’|’ball_tree’]</span></dt><dd><p>Algorithm to use for nearest neighbors search,
passed to neighbors.NearestNeighbors instance.</p>
</dd>
<dt><strong>n_jobs</strong><span class="classifier">int or None, default=None</span></dt><dd><p>The number of parallel jobs to run.
<code class="docutils literal notranslate"><span class="pre">None</span></code> means 1 unless in a <a class="reference external" href="https://joblib.readthedocs.io/en/latest/parallel.html#joblib.parallel_backend" title="(in joblib v0.14.1.dev0)"><code class="xref py py-obj docutils literal notranslate"><span class="pre">joblib.parallel_backend</span></code></a> context.
<code class="docutils literal notranslate"><span class="pre">-1</span></code> means using all processors. See <a class="reference internal" href="../../glossary.html#term-n-jobs"><span class="xref std std-term">Glossary</span></a>
for more details.</p>
</dd>
<dt><strong>metric</strong><span class="classifier">string, or callable, default=”minkowski”</span></dt><dd><p>The metric to use when calculating distance between instances in a
feature array. If metric is a string or callable, it must be one of
the options allowed by <a class="reference internal" href="sklearn.metrics.pairwise_distances.html#sklearn.metrics.pairwise_distances" title="sklearn.metrics.pairwise_distances"><code class="xref py py-func docutils literal notranslate"><span class="pre">sklearn.metrics.pairwise_distances</span></code></a> for
its metric parameter.
If metric is “precomputed”, X is assumed to be a distance matrix and
must be square. X may be a <a class="reference internal" href="../../glossary.html#term-sparse-graph"><span class="xref std std-term">Glossary</span></a>.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 0.22.</span></p>
</div>
</dd>
<dt><strong>p</strong><span class="classifier">int, default=2</span></dt><dd><p>Parameter for the Minkowski metric from
sklearn.metrics.pairwise.pairwise_distances. When p = 1, this is
equivalent to using manhattan_distance (l1), and euclidean_distance
(l2) for p = 2. For arbitrary p, minkowski_distance (l_p) is used.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 0.22.</span></p>
</div>
</dd>
<dt><strong>metric_params</strong><span class="classifier">dict, default=None</span></dt><dd><p>Additional keyword arguments for the metric function.</p>
<div class="versionadded">
<p><span class="versionmodified added">New in version 0.22.</span></p>
</div>
</dd>
</dl>
</dd>
<dt class="field-even">Attributes</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>embedding_</strong><span class="classifier">array-like, shape (n_samples, n_components)</span></dt><dd><p>Stores the embedding vectors.</p>
</dd>
<dt><strong>kernel_pca_</strong><span class="classifier">object</span></dt><dd><p><a class="reference internal" href="sklearn.decomposition.KernelPCA.html#sklearn.decomposition.KernelPCA" title="sklearn.decomposition.KernelPCA"><code class="xref py py-class docutils literal notranslate"><span class="pre">KernelPCA</span></code></a> object used to implement the
embedding.</p>
</dd>
<dt><strong>nbrs_</strong><span class="classifier">sklearn.neighbors.NearestNeighbors instance</span></dt><dd><p>Stores nearest neighbors instance, including BallTree or KDtree
if applicable.</p>
</dd>
<dt><strong>dist_matrix_</strong><span class="classifier">array-like, shape (n_samples, n_samples)</span></dt><dd><p>Stores the geodesic distance matrix of training data.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="r7f4d308f5054-1"><span class="brackets">R7f4d308f5054-1</span></dt>
<dd><p>Tenenbaum, J.B.; De Silva, V.; &amp; Langford, J.C. A global geometric
framework for nonlinear dimensionality reduction. Science 290 (5500)</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">load_digits</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sklearn.manifold</span> <span class="kn">import</span> <span class="n">Isomap</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">X</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">load_digits</span><span class="p">(</span><span class="n">return_X_y</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">X</span><span class="o">.</span><span class="n">shape</span>
<span class="go">(1797, 64)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">embedding</span> <span class="o">=</span> <span class="n">Isomap</span><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">X_transformed</span> <span class="o">=</span> <span class="n">embedding</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">[:</span><span class="mi">100</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">X_transformed</span><span class="o">.</span><span class="n">shape</span>
<span class="go">(100, 2)</span>
</pre></div>
</div>
<p class="rubric">Methods</p>
<table class="longtable docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.manifold.Isomap.fit" title="sklearn.manifold.Isomap.fit"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit</span></code></a>(self, X[, y])</p></td>
<td><p>Compute the embedding vectors for data X</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.manifold.Isomap.fit_transform" title="sklearn.manifold.Isomap.fit_transform"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fit_transform</span></code></a>(self, X[, y])</p></td>
<td><p>Fit the model from data in X and transform X.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.manifold.Isomap.get_params" title="sklearn.manifold.Isomap.get_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">get_params</span></code></a>(self[, deep])</p></td>
<td><p>Get parameters for this estimator.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.manifold.Isomap.reconstruction_error" title="sklearn.manifold.Isomap.reconstruction_error"><code class="xref py py-obj docutils literal notranslate"><span class="pre">reconstruction_error</span></code></a>(self)</p></td>
<td><p>Compute the reconstruction error for the embedding.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="#sklearn.manifold.Isomap.set_params" title="sklearn.manifold.Isomap.set_params"><code class="xref py py-obj docutils literal notranslate"><span class="pre">set_params</span></code></a>(self, \*\*params)</p></td>
<td><p>Set the parameters of this estimator.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="#sklearn.manifold.Isomap.transform" title="sklearn.manifold.Isomap.transform"><code class="xref py py-obj docutils literal notranslate"><span class="pre">transform</span></code></a>(self, X)</p></td>
<td><p>Transform X.</p></td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="sklearn.manifold.Isomap.__init__">
<code class="sig-name descname">__init__</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">n_neighbors=5</em>, <em class="sig-param">n_components=2</em>, <em class="sig-param">eigen_solver='auto'</em>, <em class="sig-param">tol=0</em>, <em class="sig-param">max_iter=None</em>, <em class="sig-param">path_method='auto'</em>, <em class="sig-param">neighbors_algorithm='auto'</em>, <em class="sig-param">n_jobs=None</em>, <em class="sig-param">metric='minkowski'</em>, <em class="sig-param">p=2</em>, <em class="sig-param">metric_params=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/manifold/_isomap.py#L126"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.manifold.Isomap.__init__" title="Permalink to this definition">¶</a></dt>
<dd><p>Initialize self.  See help(type(self)) for accurate signature.</p>
</dd></dl>

<dl class="method">
<dt id="sklearn.manifold.Isomap.fit">
<code class="sig-name descname">fit</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">X</em>, <em class="sig-param">y=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/manifold/_isomap.py#L201"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.manifold.Isomap.fit" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the embedding vectors for data X</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">{array-like, sparse graph, BallTree, KDTree, NearestNeighbors}</span></dt><dd><p>Sample data, shape = (n_samples, n_features), in the form of a
numpy array, sparse graph, precomputed tree, or NearestNeighbors
object.</p>
</dd>
<dt><strong>y</strong><span class="classifier">Ignored</span></dt><dd></dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">returns an instance of self.</span></dt><dd></dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.manifold.Isomap.fit_transform">
<code class="sig-name descname">fit_transform</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">X</em>, <em class="sig-param">y=None</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/manifold/_isomap.py#L220"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.manifold.Isomap.fit_transform" title="Permalink to this definition">¶</a></dt>
<dd><p>Fit the model from data in X and transform X.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">{array-like, sparse graph, BallTree, KDTree}</span></dt><dd><p>Training vector, where n_samples in the number of samples
and n_features is the number of features.</p>
</dd>
<dt><strong>y</strong><span class="classifier">Ignored</span></dt><dd></dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>X_new</strong><span class="classifier">array-like, shape (n_samples, n_components)</span></dt><dd></dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.manifold.Isomap.get_params">
<code class="sig-name descname">get_params</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">deep=True</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/base.py#L173"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.manifold.Isomap.get_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Get parameters for this estimator.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>deep</strong><span class="classifier">bool, default=True</span></dt><dd><p>If True, will return the parameters for this estimator and
contained subobjects that are estimators.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>params</strong><span class="classifier">mapping of string to any</span></dt><dd><p>Parameter names mapped to their values.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.manifold.Isomap.reconstruction_error">
<code class="sig-name descname">reconstruction_error</code><span class="sig-paren">(</span><em class="sig-param">self</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/manifold/_isomap.py#L177"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.manifold.Isomap.reconstruction_error" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the reconstruction error for the embedding.</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>reconstruction_error</strong><span class="classifier">float</span></dt><dd></dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>The cost function of an isomap embedding is</p>
<p><code class="docutils literal notranslate"><span class="pre">E</span> <span class="pre">=</span> <span class="pre">frobenius_norm[K(D)</span> <span class="pre">-</span> <span class="pre">K(D_fit)]</span> <span class="pre">/</span> <span class="pre">n_samples</span></code></p>
<p>Where D is the matrix of distances for the input data X,
D_fit is the matrix of distances for the output embedding X_fit,
and K is the isomap kernel:</p>
<p><code class="docutils literal notranslate"><span class="pre">K(D)</span> <span class="pre">=</span> <span class="pre">-0.5</span> <span class="pre">*</span> <span class="pre">(I</span> <span class="pre">-</span> <span class="pre">1/n_samples)</span> <span class="pre">*</span> <span class="pre">D^2</span> <span class="pre">*</span> <span class="pre">(I</span> <span class="pre">-</span> <span class="pre">1/n_samples)</span></code></p>
</dd></dl>

<dl class="method">
<dt id="sklearn.manifold.Isomap.set_params">
<code class="sig-name descname">set_params</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">**params</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/base.py#L205"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.manifold.Isomap.set_params" title="Permalink to this definition">¶</a></dt>
<dd><p>Set the parameters of this estimator.</p>
<p>The method works on simple estimators as well as on nested objects
(such as pipelines). The latter have parameters of the form
<code class="docutils literal notranslate"><span class="pre">&lt;component&gt;__&lt;parameter&gt;</span></code> so that it’s possible to update each
component of a nested object.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>**params</strong><span class="classifier">dict</span></dt><dd><p>Estimator parameters.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>self</strong><span class="classifier">object</span></dt><dd><p>Estimator instance.</p>
</dd>
</dl>
</dd>
</dl>
</dd></dl>

<dl class="method">
<dt id="sklearn.manifold.Isomap.transform">
<code class="sig-name descname">transform</code><span class="sig-paren">(</span><em class="sig-param">self</em>, <em class="sig-param">X</em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/scikit-learn/scikit-learn/blob/5f3c3f037/sklearn/manifold/_isomap.py#L238"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#sklearn.manifold.Isomap.transform" title="Permalink to this definition">¶</a></dt>
<dd><p>Transform X.</p>
<p>This is implemented by linking the points X into the graph of geodesic
distances of the training data. First the <code class="docutils literal notranslate"><span class="pre">n_neighbors</span></code> nearest
neighbors of X are found in the training data, and from these the
shortest geodesic distances from each point in X to each point in
the training data are computed in order to construct the kernel.
The embedding of X is the projection of this kernel onto the
embedding vectors of the training set.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>X</strong><span class="classifier">array-like, shape (n_queries, n_features)</span></dt><dd><p>If neighbors_algorithm=’precomputed’, X is assumed to be a
distance matrix or a sparse graph of shape
(n_queries, n_samples_fit).</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>X_new</strong><span class="classifier">array-like, shape (n_queries, n_components)</span></dt><dd></dd>
</dl>
</dd>
</dl>
</dd></dl>

</dd></dl>

<div class="section" id="examples-using-sklearn-manifold-isomap">
<h2>Examples using <code class="docutils literal notranslate"><span class="pre">sklearn.manifold.Isomap</span></code><a class="headerlink" href="#examples-using-sklearn-manifold-isomap" title="Permalink to this headline">¶</a></h2>
<div class="sphx-glr-thumbcontainer" tooltip="An illustration of dimensionality reduction on the S-curve dataset with various manifold learni..."><div class="figure align-default" id="id2">
<img alt="../../_images/sphx_glr_plot_compare_methods_thumb.png" src="../../_images/sphx_glr_plot_compare_methods_thumb.png" />
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</div><div class="sphx-glr-thumbcontainer" tooltip="An application of the different manifold techniques on a spherical data-set. Here one can see t..."><div class="figure align-default" id="id3">
<img alt="../../_images/sphx_glr_plot_manifold_sphere_thumb.png" src="../../_images/sphx_glr_plot_manifold_sphere_thumb.png" />
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</div><div class="sphx-glr-thumbcontainer" tooltip="An illustration of various embeddings on the digits dataset."><div class="figure align-default" id="id4">
<img alt="../../_images/sphx_glr_plot_lle_digits_thumb.png" src="../../_images/sphx_glr_plot_lle_digits_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/manifold/plot_lle_digits.html#sphx-glr-auto-examples-manifold-plot-lle-digits-py"><span class="std std-ref">Manifold learning on handwritten digits: Locally Linear Embedding, Isomap…</span></a></span><a class="headerlink" href="#id4" title="Permalink to this image">¶</a></p>
</div>
</div><div class="sphx-glr-thumbcontainer" tooltip="We are pleased to announce the release of scikit-learn 0.22, which comes with many bug fixes an..."><div class="figure align-default" id="id5">
<img alt="../../_images/sphx_glr_plot_release_highlights_0_22_0_thumb.png" src="../../_images/sphx_glr_plot_release_highlights_0_22_0_thumb.png" />
<p class="caption"><span class="caption-text"><a class="reference internal" href="../../auto_examples/release_highlights/plot_release_highlights_0_22_0.html#sphx-glr-auto-examples-release-highlights-plot-release-highlights-0-22-0-py"><span class="std std-ref">Release Highlights for scikit-learn 0.22</span></a></span><a class="headerlink" href="#id5" title="Permalink to this image">¶</a></p>
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